Sharraxaadda

In front of my house between my property line and the street there is a grass area. This is clearly not my property and is public property. My questions are:

1) Who's responsibility is it to maintain this area?
2) Can I do as I please with the area seeing it's in front of my house? Mulch or asphalt?
3) It is not paved or cement sidewalk, so can I legally park on it?
4) If I put down chemicals for growing plants who is liable in case someone gets hurt or poisoned from or on the area.

I would think if the town allowed me to maintain the area I would eventually own the property via Adverse Possession.

We neighbors have been debating (friendly) who's responsibility the area is.